Introduction to the task

So the story begins...

You arrive at the crime scene. A mathematics teacher has been killed on the day of the
math finals. All students and staff are present. The ordinary police officers are busy
interviewing people in order to determine exactly who were where during the time of
death and finding out who has an alibi and who has not. Your mission is to examine
the dead person and the crime scene. You are a professional crime scene investigator.
The day started out well enough, being sunny and warm with 25 degrees early on
in the morning. Later on it started to cloud over and now, at 10:00 a.m., the air temperature
reads 22.0°C. You also measure the inner temperature of the body to 30.3°C.
In order to establish the time of death of the mathematics teacher, you will need
another measurement later on. Meanwhile you closely observe the surroundings.
The mathematics teacher seem to have been stabbed in the back, and is lying in a
small back part of the schoolyard where normally no one spends much time other
than entering and exiting the school. Was the mathematics teacher going into the
building when the attack occurred? A bicycle is parked here, so that might be a reasonable
guess. The weapon is still in the wound: A papercutter type of knife was used
that can be found in almost any office. Anyone could get hold on such a papercutter.
You spray it for prints, but no luck. Wiped clean after the deed, and most likely it was
premeditated, so you note to yourself.
It must be difficult to creep up on someone in this yard, you think. Maybe the
mathematics teacher heard someone coming up from behind, but proceeded walking
without giving it a second thought. It could have been someone known to the teacher,
or maybe even a parent or some student. On an exam day like this there are many
unknown people on school grounds. People that are not normally here. Parents,
grandparents, relatives, friends, all are ready to congratulate or comfort the overtested
children …
What could be the motive for such a violent killing? An former student the teacher
had previously failed? A jealous colleague? A parent to a former student who didn’t
get into the university because of a bad math grade? Someone from the catering firm
who was annoyed because the teacher always took two glasses of milk to the food
tray despite being told not to? Right now, everyone was a suspect, except for the
janitor. Everyone wants to get in touch with the janitor on a day like this, so it would
be difficult for the janitor to get away after killing someone. It would more likely be
someone who could fly under the radar, so to speak. Someone no one would be interested
to talk to during this day. But who could that be?
Right then your captain approaches you, saying:

“Thanks to our new digital interrogation system, Comprehensive Hearings External
Additive Tally, we have managed to identify some individuals without alibi for the early
morning. Here is the list. Let me know as soon as you have an answer. I will be at the
principal’s office for the time being. The principal has helped us to organize all witness
hearings and is offering coffee, though without donuts. And be quick about it.”

You look at the printout and read...

﻿Cally Crook

﻿Parent in T14f, 48 years

﻿7:23 – 8:15

﻿Sy Smoke

﻿Catering assistant, 41 years

﻿8:38 – 8:48

﻿Charlie Bal

﻿PE teacher 30 years

﻿8:35 – 8:55

﻿Nicci Vulture

﻿Language teacher, 77 years

﻿8:50 – 9:28

﻿Alex Game

﻿Student in Sc13d, 17 years

﻿9:25 – 9:48

The main question

Right as usual, you think to yourself while you put on a sweater. Time to measure
the body temperature again. Now, at 11:00 a.m., the body temperature is
measured to 26.6°C and you start doing the arithmetic to find the precise time
when the mathematics teacher died. Based on the information available from
other teachers and the principal, the mathematics teacher was well and healthy
and could therefore be expected to have a body temperature of about 36.8°C—at
least while alive.
So back to the main question: Who killed the math teacher?